What is ln(l+sqrt(x^2+y^2))-ln(x) ?

The solution to ln(l+sqrt(x^2+y^2))-ln(x) is ln((l+sqrt(x^2+y^2))/x)

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simplify ln(l+sqrt(x^2+y^2))-ln(x)

simplify

ln (l + x^{2} + y^{2}) - ln (x)

ln (\frac{l + x ^{2} + y ^{2}}{x})

Solution steps

ln (l + x^{2} + y^{2}) - ln (x)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (l + x^{2} + y^{2}) - ln (x) = ln (\frac{l + x ^{2} + y ^{2}}{x})

= ln (\frac{l + x ^{2} + y ^{2}}{x})

- 4 (ln ∣ 2 a - 10 ∣ - ln (10))

lo g_{3} (\frac{81}{x - 9})

- ln ∣ x - 2 ∣ + ln ∣ x - 3 ∣ + C

lo g_{10} (\frac{x ^{4}}{y ^{5} z})

lo g_{2} (56) + lo g_{2} (7)

What is ln(l+sqrt(x^2+y^2))-ln(x) ?
The solution to ln(l+sqrt(x^2+y^2))-ln(x) is ln((l+sqrt(x^2+y^2))/x)